`incidenceMatrix`

Incidence matrix showing which variables appear in which equations.

Category: Mathematics > Equation Solving

Syntax

M = incidenceMatrix(eqs, vars)

Returns a 0-1 matrix with a 1 where an equation contains a variable.

Description

The matrix records only the structure of the system, not the coefficients. It is used to judge whether a DAE can be split into blocks or whether its index is high, as findDecoupledBlocks and isLowIndexDAE do.

Input arguments

eqs: Vector of symbolic equations.
vars: Vector of symbolic functions, such as [x1(t) x2(t)].

Output arguments

M: Matrix with one row per equation and one column per variable.

Example

Structure of two equations

syms x1(t) x2(t) x3(t)
eqs = [x1 + x2 == 1, x2*x3 == 0];
incidenceMatrix(eqs, [x1 x2 x3])

Output

ans = 2×3

     1     1     0
     0     1     1

See also

findDecoupledBlocks isLowIndexDAE massMatrixForm equationsToMatrix